package com.bigshen.algorithm.gTree.solution07LowestCommonAncestorOfBinaryTree;

/**
 * 236. Lowest Common Ancestor of a Binary Tree 最近公共祖先
 * Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.
 *
 * According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”
 *
 *  
 *
 * Example 1:
 * Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
 * Output: 3
 * Explanation: The LCA of nodes 5 and 1 is 3.
 *
 * Example 2:
 * Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
 * Output: 5
 * Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.
 *
 * Example 3:
 * Input: root = [1,2], p = 1, q = 2
 * Output: 1
 *
 * 来源：力扣（LeetCode）
 * 链接：https://leetcode-cn.com/problems/lowest-common-ancestor-of-a-binary-tree
 * 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。
 */
public class Solution {

    class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;
        public TreeNode(int val) {
            this.val = val;
        }
    }


    // 一个节点N，从左右两侧分别查找 p、q
    // 如果分别在两侧找到，则节点N即为最近公共祖先
    // 如果只在一侧找到，另一侧为空，则表明两个节点在同一侧
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {

        if (null == root || p == root || q == root) {
            return root;
        }

        TreeNode left = lowestCommonAncestor(root.left, p, q);
        TreeNode right = lowestCommonAncestor(root.right, p, q);

        // 找到合适值，层层上报
        if (null != left && null != right) {
            return root;
        }
        // 层层上报
        if (null != left) {
            return left;
        }
        // 层层上报
        if (null != right) {
            return right;
        }
        return null;
    }

}
